The above type of exercise apparatus is known from U.S. Pat. No. 4,759,539 in the name of the present inventor. In this prior solution, the lower section of an exercise apparatus is provided with a linkage, which is fixed relative to the exercise apparatus and elevated from the floor and around which a two-piece plane is revolved in a vertical plane for bringing the exercise apparatus into a variety of functional positions. This prior solution set forth in the patent cited above is advantageous provided that there are no restrictions set, for example, by room height. In low-ceilinged premises like basements, due to the installation of a fixed linkage above the floor, the length of a two-piece plane cannot be made functionally sufficient.